Ukrainian Engineers' Society hears presentation on optimal estimation (05/02/04)

Ukrainian Engineers' Society hears presentation on optimal estimation

by Ivan Durbak

NEW YORK - The Ukrainian Engineers' Society of New York City presented a lecture on "Optimal Estimation" by Peter Halatyn, president of KDM Aero Inc., on March 2 here at the Ukrainian Institute of America.

Mr. Halatyn combined engineering and mathematics concepts to present an informative and comprehensive look at the complex field of estimation, which he defined as "the process of extracting information from data" or, more mathematically, as "data processing methods for dealing with random variables."

After introducing the topic, Mr. Halatyn began by explaining the estimation problem, involving measurements and noise in multi-sensor systems, and noting how the different types of estimation - filtering, smoothing and predicting - have widespread applicability to thousands of real-world applications. He then went on to review the basic underlying mathematical concepts such as mean, variance, co-variance, probability, normal or gaussian probability distributions and vector matrices.

Mr. Halatyn next provided a broad historical perspective, beginning with the deterministic least-squares estimation techniques invented by Gauss (in 1809), and continuing with the work of R.A. Fisher (in 1912) with probability density functions and maximum likelihood estimation techniques. He then moved to the work of N. Wiener (in 1940), who used the frequency domain approach to design statistically optimal filters used to solve the problem of estimating signals in noise in important applications such as radar. The next and possibly most-important development was the seminal work of R.E. Kalman (in 1960) who used optimal recursive filter techniques, based on vector modeling of state-space and time-domain formulation, to develop a very efficient and robust "least-squares" estimation methodology.

Mr. Halatyn explained how the Kalman filter is now the most commonly used optimal filtering technique: for example, a recent Google search on the Internet revealed over 15,000 applications using Kalman filtering methods. These applications span a broad array of science and engineering areas, including flood prediction and atmospheric model forecasts, wireless networks, GPS pedestrian navigation, real-time estimation of human body postures, cellular networks, lidar and microwave radiometers, trace gas concentration measurements, probabilistic video stabilization, glottal closed-phase location and analysis, neural networks, weather models and even stock market forecasting.

The power of Kalman filtering lies in its ability to combine the dynamic process model with the measurement model to efficiently, recursively and robustly estimate unknown random parameters and missing states based on a sequence of noisy measurements, he said. Kalman filtering has also been extended to nonlinear models and reformulated to use functions instead of matrices.

Mr. Halatyn finished with a detailed example of the global positioning system (GPS), where a 24 satellite-based navigation system uses the linearization techniques of the extended Kalman filter to precisely locate any position on earth.

Throughout this presentation, which lasted over two hours into the night, Mr. Halatyn kept the audience engaged and involved with an artfully combined balance of highly technical material and practical real-world problem examples.

The evening finished with informal and convivial discussions over food and drinks.

Mr. Halatyn has conducted research, published recent papers and worked on practical applications using leading-edge mathematical modeling techniques that span a broad array of application areas, including cybernetics, aeronautical science, electrical engineering, navigational control and stock market forecasting. He now runs his own engineering consultant company; previously he had worked for many of the major aerospace/engineering companies, including Sikorsky, Boeing, Lockheed and Honeywell.

His lecture was the third in a series of engineering and scientific lectures presented by the Ukrainian Engineers' Society of New York during the 2003-2004 year. The lecture counted towards New York continuing education credit for licensed professional engineers.

The Ukrainian Engineers' Society of America (UESA) is an association of technical/scientific professionals and students, including engineers, scientists, architects and businesspeople. Its mission is to help advance our members' professions, foster interest in technical and economic issues in Ukraine, and provide a social and professional network of mutual support. To learn more about the UESA, readers may log on to www.uesa.org or write to UESA, 2 E. 79th St., New York, NY 10021.

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